Question

A box contains one green marble, two yellow marbles, and six pink marbles. If one marble is drawn at random, find P(green|not yellow).1/76/71/61

Answer 1

Step-by-step explanation

We are asked to resolve a conditional probability question

For the given question, we will have to find the probability of obtaining a green marble given not yellow

We have the box containing one green marble, two yellow marbles, and six pink marbles

Green = 1

Yellow = 2

Pink = 6

Probability is the ratio of the number of possible outcomes to the total outcomes

we will apply the formula

`P(G|Y^(\prime))=\frac{P(G\text{ n Y'})}{P(Y^(\prime))}`

Where

`P(G)=probability\text{ of green marble=G=}(1)/(9)`

`\begin{gathered} P(Y)=probability\text{ of Yellow = }(2)/(9) \\ \\ P(Y^(\prime))=probab\imaginaryI l\imaginaryI ty\text{ of not Yellow=1-}(2)/(9)=(7)/(9) \end{gathered}`

Thus

`\begin{gathered} P(G\text{ n }Y^(\prime))=(1)/(9) \\ \\ P(Y^(\prime))=(7)/(9) \end{gathered}`

Therefore, we will have the answer as

`P(G|Y^(\prime))=(1)/(9)/(7)/(9)=(1)/(9)*(9)/(7)=(1)/(7)`

Therefore, the answer will be

`(1)/(7)`